Electrical and Electronic Engineering - Research Publications
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ItemNo Preview AvailableTRACKING AND REGRET BOUNDS FOR ONLINE ZEROTH-ORDER EUCLIDEAN AND RIEMANNIAN OPTIMIZATION(SIAM PUBLICATIONS, 2022)
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ItemOrdinal Optimisation for the Gaussian Copula Model( 2019-11-05)We present results on the estimation and evaluation of success probabilities for ordinal optimisation over uncountable sets (such as subsets of R d ). Our formulation invokes an assumption of a Gaussian copula model, and we show that the success probability can be equivalently computed by assuming a special case of additive noise. We formally prove a lower bound on the success probability under the Gaussian copula model, and numerical experiments demonstrate that the lower bound yields a reasonable approximation to the actual success probability. Lastly, we showcase the utility of our results by guaranteeing high success probabilities with ordinal optimisation.
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ItemActive Learning for Linear Parameter-Varying System Identification( 2020-05-02)Active learning is proposed for selection of the next operating points in the design of experiments, for identifying linear parameter-varying systems. We extend existing approaches found in literature to multiple-input multiple-output systems with a multivariate scheduling parameter. Our approach is based on exploiting the probabilistic features of Gaussian process regression to quantify the overall model uncertainty across locally identified models. This results in a flexible framework which accommodates for various techniques to be applied for estimation of local linear models and their corresponding uncertainty. We perform active learning in application to the identification of a diesel engine air-path model, and demonstrate that measures of model uncertainty can be successfully reduced using the proposed framework.
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ItemTracking and regret bounds for online zeroth-order Euclidean and Riemannian optimisation( 2020-10-01)We study numerical optimisation algorithms that use zeroth-order information to minimise time-varying geodesically-convex cost functions on Riemannian manifolds. In the Euclidean setting, zeroth-order algorithms have received a lot of attention in both the time-varying and time-invariant cases. However, the extension to Riemannian manifolds is much less developed. We focus on Hadamard manifolds, which are a special class of Riemannian manifolds with global nonpositive curvature that offer convenient grounds for the generalisation of convexity notions. Specifically, we derive bounds on the expected instantaneous tracking error, and we provide algorithm parameter values that minimise the algorithm’s performance. Our results illustrate how the manifold geometry in terms of the sectional curvature affects these bounds. Additionally, we provide dynamic regret bounds for this online optimisation setting. To the best of our knowledge, these are the first regret bounds even for the Euclidean version of the problem. Lastly, via numerical simulations, we demonstrate the applicability of our algorithm on an online Karcher mean problem.
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ItemGaussian Processes with Monotonicity Constraints for Preference Learning from Pairwise Comparisons(IEEE, 2018)In preference learning, it is beneficial to incorporate monotonicity constraints for learning utility functions when there is prior knowledge of monotonicity. We present a novel method for learning utility functions with monotonicity constraints using Gaussian process regression. Data is provided in the form of pairwise comparisons between items. Using conditions on monotonicity for the predictive function, an algorithm is proposed which uses the weighted average between prior linear and maximum a posteriori (MAP) utility estimates. This algorithm is formally shown to guarantee monotonicity of the learned utility function in the dimensions desired. The algorithm is tested in a Monte Carlo simulation case study, in which the results suggest that the learned utility by the proposed algorithm performs better in prediction than the standalone linear estimate, and enforces monotonicity unlike the MAP estimate.
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ItemA machine learning approach for tuning model predictive controllers(IEEE, 2018-01-01)Many industrial domains are characterized by Multiple-Input-Multiple-Output (MIMO) systems for which an explicit relationship capturing the nontrivial trade-off between the competing objectives is not available. Human experts have the ability to implicitly learn such a relationship, which in turn enables them to tune the corresponding controller to achieve the desirable closed-loop performance. However, as the complexity of the MIMO system and/or the controller increase, so does the tuning time and the associated tuning cost. To reduce the tuning cost, a framework is proposed in which a machine learning method for approximating the human-learned cost function along with an optimization algorithm for optimizing it, and consequently tuning the controller, are employed. In this work the focus is on the tuning of Model Predictive Controllers (MPCs), given both the interest in their implementations across many industrial domains and the associated high degrees of freedom present in the corresponding tuning process. To demonstrate the proposed approach, simulation results for the tuning of an air path MPC controller in a diesel engine are presented.
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ItemA Sequential Learning Algorithm for Probabilistically Robust Controller Tuning( 2021-02-18)We introduce a sequential learning algorithm to address a robust controller tuning problem, which in effect, finds (with high probability) a candidate solution satisfying the internal performance constraint to a chance-constrained program which has black-box functions. The algorithm leverages ideas from the areas of randomised algorithms and ordinal optimisation, and also draws comparisons with the scenario approach; these have all been previously applied to finding approximate solutions for difficult design problems. By exploiting statistical correlations through black-box sampling, we formally prove that our algorithm yields a controller meeting the prescribed probabilistic performance specification. Additionally, we characterise the computational requirement of the algorithm with a probabilistic lower bound on the algorithm's stopping time. To validate our work, the algorithm is then demonstrated for tuning model predictive controllers on a diesel engine air-path across a fleet of vehicles. The algorithm successfully tuned a single controller to meet a desired tracking error performance, even in the presence of the plant uncertainty inherent across the fleet. Moreover, the algorithm was shown to exhibit a sample complexity comparable to the scenario approach.
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ItemOrdinal Optimisation and the Offline Multiple Noisy Secretary Problem( 2021-06-02)We study the success probability for a variant of the secretary problem, with noisy observations and multiple offline selection. Our formulation emulates, and is motivated by, problems involving noisy selection arising in the disciplines of stochastic simulation and simulation-based optimisation. In addition, we employ the philosophy of ordinal optimisation - involving an ordinal selection rule, and a percentile notion of goal softening for the success probability. As a result, it is shown that the success probability only depends on the underlying copula of the problem. Other general properties for the success probability are also presented. Specialising to the case of Gaussian copulas, we also derive an analytic lower bound for the success probability, which may then be inverted to find sufficiently large sample sizes that guarantee a high success probability arbitrarily close to one.
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ItemTuning of multivariable model predictive controllersthrough expert bandit feedback( 2020-02-09)For certain industrial control applications an explicit function capturing the nontrivial trade-off between competing objectives in closed loop performance is not available. In such scenarios it is common practice to use the human innate ability to implicitly learn such a relationship and manually tune the corresponding controller to achieve the desirable closed loop performance. This approach has its deficiencies because of individual variations due to experience levels and preferences in the absence of an explicit calibration metric. Moreover, as the complexity of the underlying system and/or the controller increase, in the effort to achieve better performance, so does the tuning time and the associated tuning cost. To reduce the overall tuning cost, a tuning framework is proposed herein, whereby a supervised machine learning is used to extract the human-learned cost function and an optimization algorithm that can efficiently deal with a large number of variables, is used for optimizing the extracted cost function. Given the interest in the implementation across many industrial domains and the associated high degree of freedom present in the corresponding tuning process, a Model Predictive Controller applied to air path control in a diesel engine is tuned for the purpose of demonstrating the potential of the framework.
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ItemActive Learning for Linear Parameter-Varying System Identification(ELSEVIER, 2020-01-01)Active learning is proposed for selection of the next operating points in the design of experiments, for identifying linear parameter-varying systems. We extend existing approaches found in literature to multiple-input multiple-output systems with a multivariate scheduling parameter. Our approach is based on exploiting the probabilistic features of Gaussian process regression to quantify the overall model uncertainty across locally identified models. This results in a flexible framework which accommodates for various techniques to be applied for estimation of local linear models and their corresponding uncertainty. We perform active learning in application to the identification of a diesel engine air-path model, and demonstrate that measures of model uncertainty can be successfully reduced using the proposed framework.